2026年GRE數(shù)學(xué)填空題庫及答案考試時長：120分鐘滿分：100分班級：__________姓名：__________學(xué)號：__________得分：__________試卷名稱：2026年GRE數(shù)學(xué)填空題庫及答案考核對象：準(zhǔn)備GRE數(shù)學(xué)考試的考生題型分值分布：-判斷題（總共10題，每題2分）總分20分-單選題（總共10題，每題2分）總分20分-多選題（總共10題，每題2分）總分20分-案例分析（總共3題，每題6分）總分18分-論述題（總共2題，每題11分）總分22分總分：100分---一、判斷題（每題2分，共20分）1.Thesetofintegersisclosedunderaddition.A.正確B.錯誤2.If\(f(x)=3x^2-2x+1\),then\(f(2)=f(-2)\).A.正確B.錯誤3.Theequation\(2x+3y=6\)representsalinewithaslopeof\(-\frac{2}{3}\).A.正確B.錯誤4.Afunctioncanhavemorethanonemaximumvalue.A.正確B.錯誤5.Thestandarddeviationofadatasetisalwaysgreaterthanorequaltozero.A.正確B.錯誤6.Themedianofadatasetisalwaysequaltothemean.A.正確B.錯誤7.Theprobabilityofrollingasumof7withtwosix-sideddiceis\(\frac{1}{6}\).A.正確B.錯誤8.Theareaofacirclewithradius\(r\)isgivenby\(\pir^2\).A.正確B.錯誤9.ThePythagoreantheoremappliestoalltriangles.A.正確B.錯誤10.Themodeofadatasetisalwaysunique.A.正確B.錯誤---二、單選題（每題2分，共20分）1.If\(x+y=10\)and\(x-y=4\),whatisthevalueof\(x\)?A.7B.6C.5D.32.Thevalueof\(\frac{3}{4}\div\frac{2}{3}\)is:A.\(\frac{1}{2}\)B.\(\frac{3}{8}\)C.\(\frac{9}{8}\)D.\(\frac{5}{6}\)3.Whichofthefollowingisafactorof\(x^2-9\)?A.\(x+3\)B.\(x-3\)C.BothAandBD.NeitherAnorB4.Theslopeofthelinepassingthroughthepoints\((1,2)\)and\((3,6)\)is:A.1B.2C.3D.45.If\(f(x)=x^3\),then\(f(-2)\)is:A.-8B.-6C.6D.86.Theaverageofthenumbers4,7,9,and10is:A.6.5B.7.5C.8D.97.Theequation\(x^2+6x+9=0\)has:A.OnerealsolutionB.TworealsolutionsC.NorealsolutionsD.Infinitesolutions8.Thevolumeofacubewithsidelength3is:A.9B.18C.27D.369.If\(P(A)=0.3\)and\(P(B)=0.5\),and\(A\)and\(B\)aremutuallyexclusive,then\(P(A\cupB)\)is:A.0.15B.0.5C.0.8D.0.7510.Therangeofthefunction\(f(x)=|x|\)is:A.\((-\infty,\infty)\)B.\([0,\infty)\)C.\((-1,1)\)D.\([0,1]\)---三、多選題（每題2分，共20分）1.Whichofthefollowingarepropertiesofaparallelogram?A.OppositesidesareparallelB.OppositesidesareequalinlengthC.DiagonalsbisecteachotherD.Allanglesare90degrees2.Thegraphofthefunction\(y=x^2\)is:A.AstraightlineB.AparabolaopeningupwardsC.Symmetricaboutthey-axisD.Acubicfunction3.Thefollowingnumbersarealldivisibleby3:A.12B.15C.18D.214.Themeasuresoftheanglesinatriangleare:A.30°,60°,90°B.45°,45°,90°C.60°,60°,60°D.90°,90°,90°5.Thefollowingfunctionsarelinear:A.\(y=2x+3\)B.\(y=x^2+1\)C.\(y=\frac{1}{x}\)D.\(y=5\)6.Thefollowingareexamplesofirrationalnumbers:A.\(\sqrt{2}\)B.\(\pi\)C.\(\frac{3}{4}\)D.\(0.1010010001\ldots\)7.Thefollowingarepropertiesofacircle:A.AllradiiareequalB.ThedistancefromthecentertoanypointonthecircleisconstantC.Thecircumferenceisgivenby\(2\pir\)D.Theareaisgivenby\(\pir^2\)8.Thefollowingaretypesofprobabilitydistributions:A.NormaldistributionB.BinomialdistributionC.PoissondistributionD.Exponentialdistribution9.Thefollowingareexamplesofgeometricsequences:A.2,4,8,16,...B.3,6,12,24,...C.5,5,5,5,...D.1,3,5,7,...10.Thefollowingarepropertiesofafunction:A.ItassignseachinputtoexactlyoneoutputB.ItcanhavemultipleinputsforasingleoutputC.Ithasawell-defineddomainandrangeD.Itisalwayscontinuous---四、案例分析（每題6分，共18分）1.Acompanyproducestwotypesoftoys:AandB.EachtoyArequires2unitsofplasticand1unitoffabric,whileeachtoyBrequires1unitofplasticand2unitsoffabric.Thecompanyhas100unitsofplasticand80unitsoffabricavailable.IftheprofitfromeachtoyAis$3andfromeachtoyBis$4,howmanyofeachtypeoftoyshouldthecompanyproducetomaximizeprofit?2.Abagcontains5redballs,4blueballs,and3greenballs.Iftwoballsaredrawnatrandomwithoutreplacement,whatistheprobabilitythatbothballsareofthesamecolor?3.Thetemperatureinacityfollowsanormaldistributionwithameanof25°Candastandarddeviationof5°C.Whatistheprobabilitythatthetemperatureisabove30°C?---五、論述題（每題11分，共22分）1.Explainthedifferencebetweenmean,median,andmode.Provideanexampleofadatasetwherethesemeasuresaredifferentanddiscusswhy.2.Describethepropertiesofafunctionandprovideanexampleofafunctionthatdemonstrateseachproperty.Howdoestheconceptofafunctionapplytoreal-worldscenarios?---標(biāo)準(zhǔn)答案及解析---一、判斷題1.A.正確解析：整數(shù)集在加法下是封閉的，即任意兩個整數(shù)的和仍然是整數(shù)。2.B.錯誤解析：\(f(2)=3(2)^2-2(2)+1=9\)，\(f(-2)=3(-2)^2-2(-2)+1=13\)，兩者不相等。3.B.錯誤解析：該方程的斜率為\(-\frac{2}{3}\)，但正確表達(dá)應(yīng)為\(y=-\frac{2}{3}x+2\)。4.A.正確解析：函數(shù)可以有多重局部最大值，例如\(f(x)=-x^4+2x^2\)在\(x=-1\)和\(x=1\)處都有局部最大值。5.A.正確解析：標(biāo)準(zhǔn)差是數(shù)據(jù)分散程度的度量，因此始終非負(fù)。6.B.錯誤解析：均值和中位數(shù)只有在數(shù)據(jù)對稱分布時才相等。7.B.錯誤解析：兩顆六面骰子擲出和為7的概率為\(\frac{6}{36}=\frac{1}{6}\)，但和為7的組合有6種（1+6,2+5,3+4,4+3,5+2,6+1）。8.A.正確解析：圓的面積公式為\(\pir^2\)。9.B.錯誤解析：勾股定理僅適用于直角三角形。10.B.錯誤解析：數(shù)據(jù)集可以有多個眾數(shù)，例如數(shù)據(jù)集{1,1,2,3}的眾數(shù)是1和2。---二、單選題1.A.7解析：聯(lián)立方程\(x+y=10\)和\(x-y=4\)，解得\(x=7\)。2.C.\(\frac{9}{8}\)解析：\(\frac{3}{4}\div\frac{2}{3}=\frac{3}{4}\times\frac{3}{2}=\frac{9}{8}\)。3.C.BothAandB解析：\(x^2-9=(x+3)(x-3)\)。4.B.2解析：斜率\(m=\frac{6-2}{3-1}=2\)。5.A.-8解析：\(f(-2)=(-2)^3=-8\)。6.B.7.5解析：平均數(shù)\(\frac{4+7+9+10}{4}=7.5\)。7.B.Tworealsolutions解析：判別式\(\Delta=6^2-4\times1\times9=0\)，有兩個相等的實(shí)根。8.C.27解析：體積\(3^3=27\)。9.C.0.8解析：\(P(A\cupB)=P(A)+P(B)=0.3+0.5=0.8\)。10.B.\([0,\infty)\)解析：絕對值函數(shù)的值域?yàn)榉秦?fù)實(shí)數(shù)。---三、多選題1.A,B,C解析：平行四邊形的性質(zhì)包括對邊平行、相等且對角線互相平分。2.B,C解析：\(y=x^2\)是開口向上的拋物線，且關(guān)于y軸對稱。3.A,B,C,D解析：12,15,18,21均能被3整除。4.A,B,C解析：三角形的內(nèi)角和為180°，但只有A、B、C是常見類型。5.A,D解析：\(y=2x+3\)和\(y=5\)是線性函數(shù)。6.A,B,D解析：\(\sqrt{2}\)、\(\pi\)和無理數(shù)序列\(zhòng)(0.1010010001\ldots\)是無理數(shù)。7.A,B,C,D解析：均為圓的性質(zhì)。8.A,B,C,D解析：均為常見概率分布。9.A,B解析：2,4,8,...和3,6,12,...是幾何序列。10.A,C解析：函數(shù)的定義要求單值映射且具有定義域和值域。---四、案例分析1.解題思路：-設(shè)生產(chǎn)玩具A的數(shù)量為\(x\)，玩具B的數(shù)量為\(y\)。-目標(biāo)函數(shù)：\(3x+4y\)（利潤最大化）。-約束條件：\(2x+y\leq100\)（塑料）\(x+2y\leq80\)（布料）\(x\geq0,y\geq0\)-解法：圖解法或線性規(guī)劃。-最優(yōu)解：\(x=40\)，\(y=20\)，最大利潤為\(3\times40+4\times20=200\)。2.解題思路：-總球